Problem: Express this quotient in scientific notation: ${\frac{1.620\times 10^{3}} {9.0\times 10^{2}}}$
Start by collecting like terms together. $= {\frac{1.620} {9.0}} \times{\frac{10^{3}} {10^{2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.18 \times 10^{3\,-\,2}$ $= 0.18 \times 10^{1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.18$ is the same as $1.80 \div 10$ , or $1.80 \times 10^{-1}$ $ = {1.80 \times 10^{-1}} \times 10^{1} $ $= 1.80\times 10^{0}$